The material point moves in the plane uniformly and linearly according to the law according to the coordinate

The material point moves in the plane uniformly and linearly according to the law according to the coordinate system x = 4 + 3t; y = 3-4t. What is the magnitude of the point’s velocity?

Given:

x (t) = 4 + 3 * t – dependence of the X coordinate on time;

y (t) = 3 – 4 * t – the dependence of the change in the Y coordinate on time.

It is required to determine the speed of a material point v (m / s).

According to the condition of the problem, the body moves uniformly, that is, with a constant speed.

Let’s find the coordinates of the body at the time t = 0.

x0 = 4 + 3 * 0 = 4.

y0 = 3 – 4 * 0 = 3.

Let’s find the coordinates of the body at the time t1 = 1.

x1 = 4 + 3 * 1 = 4 + 3 = 7.

y1 = 3 – 4 * 1 = 3 – 4 = -1.

Then the movement of the body along the X axis will be equal to:

S1 = x1 – x0 = 7 – 4 = 3 meters.

Moving along the Y axis will be equal to:

S2 = Y1 – Y0 = -1 – 3 = -4.

The total distance covered in 1 second is:

S = (S1 ^ 2 + S2 ^ 2) ^ 0.5 = (3 ^ 2 + (-4) ^ 2) ^ 0.5 = (9 + 16) ^ 0.5 = 25 ^ 0.5 = 5 …

Then the speed of the body will be equal to:

v = S / t1 = 5/1 = 5 m / s.

Answer: the speed of the body is 5 meters per second.